Whitney tower concordance of classical links

Conant, James¹ ; Schneiderman, Rob² ; Teichner, Peter³

¹ Department of Mathematics, University of Tennessee, Knoxville TN 37996, USA
² Department of Mathematics and Computer Science, Lehman College, CUNY, Bronx NY 10468-1589, USA
³ Department of Mathematics, University of California, Berkeley, Berkeley CA 94720-3840, USA, Max-Planck Institut für Mathematik, Bonn, Germany

Geometry & topology, Tome 16 (2012) no. 3, pp. 1419-1479.

Résumé

This paper computes Whitney tower filtrations of classical links. Whitney towers consist of iterated stages of Whitney disks and allow a tree-valued intersection theory, showing that the associated graded quotients of the filtration are finitely generated abelian groups. Twisted Whitney towers are studied and a new quadratic refinement of the intersection theory is introduced, measuring Whitney disk framing obstructions. It is shown that the filtrations are completely classified by Milnor invariants together with new higher-order Sato–Levine and higher-order Arf invariants, which are obstructions to framing a twisted Whitney tower in the $4$–ball bounded by a link in the $3$–sphere. Applications include computation of the grope filtration and new geometric characterizations of Milnor’s link invariants.

Détail

DOI : 10.2140/gt.2012.16.1419

Classification : 57M25, 57M27, 57Q60, 57N10
Keywords: Whitney tower, grope, link concordance, tree, higher-order Arf invariant, higher-order Sato–Levine invariant, twisted Whitney disk

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